Generating Ideals in Rings of Integer-Valued Polynomials

http://dx.doi.org/10.4153/CMB-1999-028-0
Canad. Math. Bull. 42(1999), 231-236

  Published:1999-06-01
 Printed: Jun 1999

Let $R$ be a one-dimensional locally analytically irreducible Noetherian domain with finite residue fields. In this note it is shown that if $I$ is a finitely generated ideal of the ring $\Int(R)$ of integer-valued polynomials such that for each $x \in R$ the ideal $I(x) =\{f(x) \mid f \in I\}$ is strongly $n$-generated, $n \geq 2$, then $I$ is $n$-generated, and some variations of this result.